Disable incoming requests on Public IP

Set up a droplet having the private networking option enabled. My aim is to:
1) Keep internet available on the droplet (so killing eth0 interface is not an option).
2) Block all incoming traffic from the internet.
3) Communicate with the droplet using the private IP (from another droplet).

I tried both these iptables (flipped order between two options), to absolutely no avail: